Clementine It is strange this decision to keep the milk and honey and not to be able to say 'vegan'. Maybe it is the choice because the word vegan would push away some existing customers, it is a word that divides the people sometimes.
I don't think that is the reason, if you are going to pay to go this kind of restaurant most people will order a 'tasting menu' and eat whatever it is that the chef has decided they should eat, you are paying for the ideas and the artistry.
Maybe they just really think that milk and honey is what makes their coffee and tea taste the best and don't want to compromise on that. Personally I think honey in coffee is strange and wrong but I'm sure many people would disagree.